Chapter 23: The Electric Field

The permanent electric dipole moment of the water molecule $\left({\mathrm{H}}_2\mathrm{O}\right)$ is $6.2\times {10}^{-30}\mathrm{Cm}$. What is the maximum possible torque on a water molecule in a $5.0\times {10}^8\mathrm{N}/\mathrm{C}$electric field?

A point charge $\overline{Q}$is distance r from a dipole consisting of charges$\pm q$separated by distance sT e dipole is initially oriented so that Q is in the plane bisecting the dipole. Immediately after the dipole is released, what are (a) the magnitude of the force and (b) the magnitude of the torque on the dipole? You can assume

An ammonia molecule$N{H}_3$ has a permanent electric dipole moment$5.0\times {10}^{30}Cm$. A proton is $2.0nm$ from the molecule in the plane that bisects the dipole. What is the electric force of the molecule on the proton?

What are the strength and direction of the electric field at the position indicated by the dot in FIGURE P$23.35$? Give your answer (a) in component form and (b) as a magnitude and angle measured cw or ccw (specify which) from the positive $x$-axis.

What are the strength and direction of the electric field at the position indicated by the dot in $FIGUREP23.36$? Give your answer $\left(a\right)$in component form and $\left(b\right)$as a magnitude and angle measured $cw$or $ccw$(specify which) from the positive $x$-axis.

What are the strength and direction of the electric field at the position indicated by the dot in $FIGUREP23.37$? Give your answer $\left(a\right)$in component form and $\left(b\right)$as a magnitude and angle measured $cw$or $ccw$(specify which) from the positive $x$-axis.

$FIGUREP23.38$shows three charges at the corners of a square. Write the electric field at point $P$in component form.

What are the strength and direction of the electric field at the position indicated by the dot in FIGURE EX23.4? Specify the direction as an angle above or below horizontal

A small segment of wire in FIGURE $Q23.4$contains $10nC$of charge.

a. The segment is shrunk to one-third of its original length. What is the ratio of ${\lambda }_f/{\lambda }_i$, where ${\lambda }_{i}and{\lambda }_f$ are the initial and final linear charge densities?

b. A proton is very far from the wire. What is the ratio Ff /Fi of the electric force on the proton after the segment is shrunk to the force before the segment was shrunk?

c. Suppose the original segment of wire is stretched to $10$ times its original length. How much charge must be added to the wire to keep the linear charge density unchanged?

$FIGUREP23.41$ is a cross section of two infinite lines of charge that extend out of the page. Both have linear charge density $\lambda$. Find an expression for the electric field strength $E$ at height $y$ above the midpoint between the lines.